Using the Pythagorean Theorem, which of the following is true?

A
The sum of the areas of squares B and C is

equal to the area of square A.

B
The sum of the areas of squares A and C is

equal to the area of square B.

C
The sum of the areas of squares A and B is

equal to the area of square C.

D
The difference of the areas of squares A and

B is equal to the area of square C.

1 answer

The Pythagorean Theorem states that in a right triangle, the sum of the areas of the squares on the two legs (sides A and B) is equal to the area of the square on the hypotenuse (side C). This can be expressed mathematically as:

\[ A^2 + B^2 = C^2 \]

Where:

  • \( A \) and \( B \) are the lengths of the legs of the right triangle,
  • \( C \) is the length of the hypotenuse.

Given the options you've presented:

  • Option A states that the sum of the areas of squares B and C equals the area of square A. (Incorrect)
  • Option B states that the sum of the areas of squares A and C equals the area of square B. (Incorrect)
  • Option C states that the sum of the areas of squares A and B equals the area of square C. (Correct)
  • Option D states that the difference of the areas of squares A and B is equal to the area of square C. (Incorrect)

Thus, the correct answer is:

C: The sum of the areas of squares A and B is equal to the area of square C.